NCERT SOLUTIONS FOR CLASS 8 MATHS CHAPTER 9 ALGEBRAIC EXPRESSIONS AND IDENTITIES

The National Council of Educational Research and Training (NCERT) is an autonomous body of the Indian government that formulates the curricula for schools in India that are governed by the Central Board of Secondary Education (CBSE) and certain state boards. Therefore, students who will be taking the Class 10 tests administered by various boards should consult this NCERT Syllabus in order to prepare for those examinations, which in turn will assist those students get a passing score.

You can also download the NCERT SOLUTIONS FOR CLASS 8 MATHS CHAPTER 9 ALGEBRAIC EXPRESSIONS AND IDENTITIES to assist you in comprehensively reviewing the course material and achieving a higher score on your upcoming assessments.

Students are able to create a strong conceptual basis with the help of the NCERT Solutions PDFs available at SWC. This base plays a key part in the students’ preparation for the latter phases of the competitive examinations. We give comprehensive answers to challenges posed by NCERT in accordance with the methodology provided by CBSE. The students are able to effortlessly prepare all of the ideas that are presented in their respective courses better and more successfully, and they are even able to succeed in passing the most difficult competitive examinations, such as JEE Main, JEE Advanced, NEET, AIMS, and so on.

Your academic journey begins a new stage as you reach the eighth grade, and a new facet of learning awaits you. This is the year where pupils begin to acquire an interest in the topic at hand, and it is also the year in which you choose whether you will study business, humanity, or science in the following year (class 12). As a consequence of this, having a solid foundation of knowledge in fields such as mathematics and physics comes highly recommended. The NCERT textbook for class 8 is the greatest book now available on the market for enhancing one’s education in the areas of mathematics and science. Read up on the theory that is presented in the book for grade 8 and answer all of the questions that are posed in the practice section of the NCERT textbook.

NCERT SOLUTIONS FOR CLASS 8 MATHS CHAPTER 9 ALGEBRAIC EXPRESSIONS AND IDENTITIES – Exercises

NCERT Solutions for Class 8 Maths Exercise 9.1

Question 1.

Identify the terms, their coefficients for each of the following expressions:

(i)  Algebraic Expressions and Identities/image001.png    ncert solution

(ii)    1 + x + x²

(iii) Algebraic Expressions and Identities/image003.png   

(iv)  3 – pq + qr -rp

(v)     ncert solution + ncert solution – xy

(vi) 3 – pq + qr -rp

Solution :

(i) Terms: Algebraic Expressions and Identities/image007.png and ncert solution

Coefficient in Algebraic Expressions and Identities/image007.png is 5 and in ncert solution is  -3

(ii) Terms: 1, x and x²

Coefficient of Algebraic Expressions and Identities/image007.png and coefficient of x²  is 1.

(iii) Terms: Algebraic Expressions and Identities/image014.png and  z²

Coefficient in Algebraic Expressions and Identities/image016.pngis 4, coefficient of Algebraic Expressions and Identities/image017.png is -4  and coefficient of  is 1.

(iv) Terms:  3, -pq, qr  and -rp

Coefficient of -pq is -1, coefficient of qr is 1 and coefficient of -rp is Algebraic Expressions and Identities/image025.png

(v) Terms: Algebraic Expressions and Identities/image026.png and  -xy

Coefficient of Algebraic Expressions and Identities/image028.png isAlgebraic Expressions and Identities/image029.png coefficient of Algebraic Expressions and Identities/image030.pngis Algebraic Expressions and Identities/image029.png and coefficient of -xy is -1.

(vi) Terms:  0.3a, -0.6ab  and 0.5b

Coefficient of 0.3a  is 0.3, coefficient of -0.6ab  is -0.6 and coefficient of 0.5b  is 0.5.

Question 2.

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:

Algebraic Expressions and Identities/image037.png
Algebraic Expressions and Identities/image038.png

Solution :

 (i) Since Algebraic Expressions and Identities/image049.png contains two terms. Therefore it is binomial.

(ii) Since 1000 contains one terms. Therefore it is monomial.

(iii) Since Algebraic Expressions and Identities/image049.pngcontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(iv) SinceAlgebraic Expressions and Identities/image051.png contains three terms. Therefore it is trinomial.

(v) Since Algebraic Expressions and Identities/image052.png contains two terms. Therefore it is binomial.

(vi) SinceAlgebraic Expressions and Identities/image053.png contains three terms. Therefore it is trinomial.

(vii) Since Algebraic Expressions and Identities/image054.pngcontains three terms. Therefore it is trinomial.

(viii) Since Algebraic Expressions and Identities/image055.pngcontains two terms. Therefore it is binomial.

(ix) Since Algebraic Expressions and Identities/image056.pngcontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(x) Since pqr contains one terms. Therefore it is monomial.

(xi) Since Algebraic Expressions and Identities/image058.pngcontains two terms. Therefore it is binomial.

(xii) Since  2p + 2q contains two terms. Therefore it is binomial.

Question 3.

Add the following:

(i)Algebraic Expressions and Identities/image059.png

(ii)Algebraic Expressions and Identities/image060.png

(iii)Algebraic Expressions and Identities/image061.png

(iv) Algebraic Expressions and Identities/image062.png

Solution :

 (i)Algebraic Expressions and Identities/image059.png

Algebraic Expressions and Identities/image063.png
Algebraic Expressions and Identities/image064.png

Hence the sum if 0.

Hence the sum is  ab + ac + bc.

Algebraic Expressions and Identities/image067.png

Question 4.

Algebraic Expressions and Identities/image073.png

Solution :

Algebraic Expressions and Identities/image079.png

NCERT Solutions for Class 8 Maths Exercise 9.2

Question 1.

Find the product of the following pairs of monomials:

(i)     Algebraic Expressions and Identities/image001.png

(ii)  Algebraic Expressions and Identities/image003.png   

(iii) Algebraic Expressions and Identities/image003.png

(iv) Algebraic Expressions and Identities/image004.png   

(iv) 4p ,0

Solution :

(i)   Algebraic Expressions and Identities/image006.png = Algebraic Expressions and Identities/image007.png = Algebraic Expressions and Identities/image008.png

(ii)Algebraic Expressions and Identities/image003.png = Algebraic Expressions and Identities/image010.png

Algebraic Expressions and Identities/image011.png

(iii) Algebraic Expressions and Identities/image012.pngAlgebraic Expressions and Identities/image013.png

Algebraic Expressions and Identities/image014.png

(iv)Algebraic Expressions and Identities/image015.png =Algebraic Expressions and Identities/image016.png

Algebraic Expressions and Identities/image017.png

(v)Algebraic Expressions and Identities/image018.pngAlgebraic Expressions and Identities/image019.png = 0

Question 2.

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:

Algebraic Expressions and Identities/image020.png

Solution :

 (i)   Area of rectangle

=Algebraic Expressions and Identities/image021.png

=Algebraic Expressions and Identities/image022.png sq. units

(ii) Area of rectangle

=Algebraic Expressions and Identities/image021.png

Algebraic Expressions and Identities/image023.png

50mn sq. units

(iii) Area of rectangle  =Algebraic Expressions and Identities/image021.png

Algebraic Expressions and Identities/image025.png

Algebraic Expressions and Identities/image022.pngsq. units

(iv) Area of rectangle  =Algebraic Expressions and Identities/image021.png

Algebraic Expressions and Identities/image027.png

Algebraic Expressions and Identities/image028.png sq. units

(v) Area of rectangle  =Algebraic Expressions and Identities/image021.png

Algebraic Expressions and Identities/image029.png

Algebraic Expressions and Identities/image024.png sq. units

Question 3.

Complete the table of products:

(i)
Algebraic Expressions and Identities/image094.PNG    

Solution :

(i)
Algebraic Expressions and Identities/image095.PNG    

Question 4.

Obtain the volume of rectangular boxes with the following length, breadth and height respectively:

(i)    Algebraic Expressions and Identities/image061.png    

(ii) Algebraic Expressions and Identities/image062.png

(iii) Algebraic Expressions and Identities/image063.png    

(iv) Algebraic Expressions and Identities/image064.png

Solution :

(i) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

=Algebraic Expressions and Identities/image066.png

=Algebraic Expressions and Identities/image067.pngcubic units

(ii) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

=Algebraic Expressions and Identities/image068.png

=Algebraic Expressions and Identities/image069.png cubic units

(iii) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

=Algebraic Expressions and Identities/image068.png

Algebraic Expressions and Identities/image071.png

=Algebraic Expressions and Identities/image072.pngcubic units

(iv) Volume of rectangular box

=Algebraic Expressions and Identities/image065.png

Algebraic Expressions and Identities/image074.png cubic units

Question 5.

Obtain the product of:

(i)    Algebraic Expressions and Identities/image075.png

(ii) Algebraic Expressions and Identities/image076.png

(iii) Algebraic Expressions and Identities/image077.png   

(iv) Algebraic Expressions and Identities/image078.png

(v) Algebraic Expressions and Identities/image079.png

Solution :

(i)  Algebraic Expressions and Identities/image080.png

Algebraic Expressions and Identities/image081.png

(ii) Algebraic Expressions and Identities/image082.pngAlgebraic Expressions and Identities/image083.png

Algebraic Expressions and Identities/image084.png

(iii) Algebraic Expressions and Identities/image085.png
Algebraic Expressions and Identities/image086.png

Algebraic Expressions and Identities/image087.png

(iv)Algebraic Expressions and Identities/image088.png

Algebraic Expressions and Identities/image089.png

=Algebraic Expressions and Identities/image090.png

(v) Algebraic Expressions and Identities/image091.pngAlgebraic Expressions and Identities/image092.png

Algebraic Expressions and Identities/image093.png

NCERT Solutions for Class 8 Maths Exercise 9.3

Question 1.

Carry out the multiplication of the expressions in each of the following pairs:

(i)  Algebraic Expressions and Identities/image001.png

(ii) Algebraic Expressions and Identities/image003.png

(iii) Algebraic Expressions and Identities/image004.png

(iv) Algebraic Expressions and Identities/image004.png

(v)  Algebraic Expressions and Identities/image005.png

Solution :

(i)Algebraic Expressions and Identities/image006.png

Algebraic Expressions and Identities/image007.png

(ii)Algebraic Expressions and Identities/image008.png

Algebraic Expressions and Identities/image009.png

(iii)Algebraic Expressions and Identities/image010.png

Algebraic Expressions and Identities/image011.png

(iv)Algebraic Expressions and Identities/image012.png

Algebraic Expressions and Identities/image013.png

 (v)Algebraic Expressions and Identities/image014.png = Algebraic Expressions and Identities/image015.png

= 0 + 0 + 0 = 0

Question 2.

Complete the table:

Algebraic Expressions and Identities/image013.png

Solution :

Algebraic Expressions and Identities/image013.png
Algebraic Expressions and Identities/image013.png

Question 3.

Find the product:

(i)  Algebraic Expressions and Identities/image041.png

(ii) Algebraic Expressions and Identities/image042.png

(iii) Algebraic Expressions and Identities/image043.png

(iv) Algebraic Expressions and Identities/image044.png

Solution :

 (i)Algebraic Expressions and Identities/image045.png

Algebraic Expressions and Identities/image046.png

Algebraic Expressions and Identities/image047.png

(ii) Algebraic Expressions and Identities/image042.png

Algebraic Expressions and Identities/image048.png

Algebraic Expressions and Identities/image049.png

(iii)Algebraic Expressions and Identities/image050.png

Algebraic Expressions and Identities/image051.png

Algebraic Expressions and Identities/image052.png

(iv) Algebraic Expressions and Identities/image053.png =Algebraic Expressions and Identities/image054.png

Question 4.

(a) Simplify: Algebraic Expressions and Identities/image055.pngand find values for

(i) Algebraic Expressions and Identities/image056.png

(ii) Algebraic Expressions and Identities/image057.png

(b) Simplify: Algebraic Expressions and Identities/image058.png find its value for

(i) Algebraic Expressions and Identities/image059.png

(ii) Algebraic Expressions and Identities/image060.png

(iii) Algebraic Expressions and Identities/image061.png

Solution :

(a) Algebraic Expressions and Identities/image055.png

Algebraic Expressions and Identities/image062.png

Algebraic Expressions and Identities/image063.png

(i) For Algebraic Expressions and Identities/image064.pngAlgebraic Expressions and Identities/image065.png

Algebraic Expressions and Identities/image066.png

Algebraic Expressions and Identities/image067.png= 108 – 45 + 3 = 66

(ii) For Algebraic Expressions and Identities/image068.pngAlgebraic Expressions and Identities/image063.png

Algebraic Expressions and Identities/image069.png

Algebraic Expressions and Identities/image070.png

Algebraic Expressions and Identities/image071.png

(b)Algebraic Expressions and Identities/image058.png

Algebraic Expressions and Identities/image072.png

Algebraic Expressions and Identities/image073.png

(i)  For  a= 0, Algebraic Expressions and Identities/image073.png

Algebraic Expressions and Identities/image075.png

= 0 + 0 + 0 + 5 = 5

(ii) For a = 1 Algebraic Expressions and Identities/image073.png

Algebraic Expressions and Identities/image077.png

= 1 + 1 + 1 + 5 = 8

(iii) For Algebraic Expressions and Identities/image078.pngAlgebraic Expressions and Identities/image073.png

Algebraic Expressions and Identities/image079.png

=  Algebraic Expressions and Identities/image080.png=Algebraic Expressions and Identities/image081.png =4

Question 5.

(a) Add: Algebraic Expressions and Identities/image082.png and Algebraic Expressions and Identities/image083.png

(b) Add:Algebraic Expressions and Identities/image084.pngand Algebraic Expressions and Identities/image085.png

(c) Subtract: Algebraic Expressions and Identities/image086.png from Algebraic Expressions and Identities/image087.png

(d) Subtract: Algebraic Expressions and Identities/image088.pngfrom Algebraic Expressions and Identities/image089.png

Solution :

(a)Algebraic Expressions and Identities/image090.png

=Algebraic Expressions and Identities/image091.png

=Algebraic Expressions and Identities/image092.png

(b)Algebraic Expressions and Identities/image093.pngc9m9thCh49(1)

=Algebraic Expressions and Identities/image094.png

=Algebraic Expressions and Identities/image095.png

=Algebraic Expressions and Identities/image096.png

(c)Algebraic Expressions and Identities/image097.png

=Algebraic Expressions and Identities/image098.png

=Algebraic Expressions and Identities/image099.png

=Algebraic Expressions and Identities/image100.png

(d)Algebraic Expressions and Identities/image101.png

=Algebraic Expressions and Identities/image102.png

=Algebraic Expressions and Identities/image103.png

=Algebraic Expressions and Identities/image104.png

=Algebraic Expressions and Identities/image105.png

=Algebraic Expressions and Identities/image106.png

=Algebraic Expressions and Identities/image107.png

NCERT Solutions for Class 8 Maths Exercise 9.4

Question 1.

Multiply the binomials:

(i)Algebraic Expressions and Identities/image001.png and Algebraic Expressions and Identities/image002.png

(ii) Algebraic Expressions and Identities/image003.png and Algebraic Expressions and Identities/image006.png

(iii) Algebraic Expressions and Identities/image005.png and Algebraic Expressions and Identities/image006.png

(iv) image007.pngand image008.png

(v) Algebraic Expressions and Identities/image009.png and Algebraic Expressions and Identities/image010.png

(vi) Algebraic Expressions and Identities/image011.png and Algebraic Expressions and Identities/image012.png

Solution :

(i) Algebraic Expressions and Identities/image013.png

Algebraic Expressions and Identities/image014.png

Algebraic Expressions and Identities/image015.png

Algebraic Expressions and Identities/image016.png

Algebraic Expressions and Identities/image017.png

(ii)Algebraic Expressions and Identities/image018.png

=Algebraic Expressions and Identities/image019.png

=Algebraic Expressions and Identities/image020.png

=Algebraic Expressions and Identities/image021.png

(iii)Algebraic Expressions and Identities/image022.png

Algebraic Expressions and Identities/image023.png

=Algebraic Expressions and Identities/image024.png

=Algebraic Expressions and Identities/image025.png

=Algebraic Expressions and Identities/image026.png

(iv)Algebraic Expressions and Identities/image027.png

=Algebraic Expressions and Identities/image028.png

=Algebraic Expressions and Identities/image029.png

(v)Algebraic Expressions and Identities/image030.png

=Algebraic Expressions and Identities/image031.png

=Algebraic Expressions and Identities/image031.png

=Algebraic Expressions and Identities/image033.png

=Algebraic Expressions and Identities/image034.png

(vi)Algebraic Expressions and Identities/image035.png

Algebraic Expressions and Identities/image036.png
Algebraic Expressions and Identities/image037.png

=Algebraic Expressions and Identities/image038.png

=Algebraic Expressions and Identities/image039.png

=Algebraic Expressions and Identities/image040.png

Question 2.

Find the product:

(i)  Algebraic Expressions and Identities/image041.png

(ii) Algebraic Expressions and Identities/image042.png

(iii) Algebraic Expressions and Identities/image043.png

(iv)  Algebraic Expressions and Identities/image044.png

Solution :

(i)Algebraic Expressions and Identities/image041.png

Algebraic Expressions and Identities/image045.png

=Algebraic Expressions and Identities/image046.png

Algebraic Expressions and Identities/image047.png= 15 – x -2x²

(ii)Algebraic Expressions and Identities/image042.png

Algebraic Expressions and Identities/image049.png

=Algebraic Expressions and Identities/image050.png

=Algebraic Expressions and Identities/image052.png

(iii)Algebraic Expressions and Identities/image043.png

Algebraic Expressions and Identities/image053.png

=Algebraic Expressions and Identities/image054.png

=Algebraic Expressions and Identities/image055.png

(iv)Algebraic Expressions and Identities/image044.png

Algebraic Expressions and Identities/image056.png

=Algebraic Expressions and Identities/image057.png

=Algebraic Expressions and Identities/image058.png

Question 3.

Simplify:

(i)Algebraic Expressions and Identities/image059.png

(ii)Algebraic Expressions and Identities/image060.png

(iii)Algebraic Expressions and Identities/image061.png

(iv)Algebraic Expressions and Identities/image062.png

(v)Algebraic Expressions and Identities/image063.png

(vi)Algebraic Expressions and Identities/image064.png

(vii)Algebraic Expressions and Identities/image065.png

(viii)Algebraic Expressions and Identities/image066.png

Solution :

(i)Algebraic Expressions and Identities/image067.png

Algebraic Expressions and Identities/image068.png

=Algebraic Expressions and Identities/image069.png

=Algebraic Expressions and Identities/image070.png

=Algebraic Expressions and Identities/image071.png

(ii)Algebraic Expressions and Identities/image072.png

Algebraic Expressions and Identities/image073.png

=Algebraic Expressions and Identities/image074.png

=Algebraic Expressions and Identities/image075.png

=Algebraic Expressions and Identities/image076.png

(iii)Algebraic Expressions and Identities/image077.png

=Algebraic Expressions and Identities/image078.png

=Algebraic Expressions and Identities/image079.png

(iv)Algebraic Expressions and Identities/image080.png

Algebraic Expressions and Identities/image081.png

=Algebraic Expressions and Identities/image082.png

=Algebraic Expressions and Identities/image083.png

=Algebraic Expressions and Identities/image084.png

= 4ac

(v)Algebraic Expressions and Identities/image086.png

Algebraic Expressions and Identities/image087.png

=Algebraic Expressions and Identities/image088.png

=Algebraic Expressions and Identities/image089.png

=Algebraic Expressions and Identities/image090.png

(vi)Algebraic Expressions and Identities/image091.png

Algebraic Expressions and Identities/image092.png

=Algebraic Expressions and Identities/image093.png

=Algebraic Expressions and Identities/image095.png

(vii)Algebraic Expressions and Identities/image096.png

Algebraic Expressions and Identities/image097.png

=Algebraic Expressions and Identities/image098.png

=Algebraic Expressions and Identities/image094.png

=Algebraic Expressions and Identities/image100.png

(viii)Algebraic Expressions and Identities/image096.png

Algebraic Expressions and Identities/image102.png

=Algebraic Expressions and Identities/image103.png

=Algebraic Expressions and Identities/image104.png

=Algebraic Expressions and Identities/image105.png

Conclusions for NCERT Solutions Class 8 Maths Chapter 9

The academic team has provided NCERT answers for class 8 mathematics chapter-9. We’ve given solutions for all of Chapter 9’s exercises. These are step-by-step answers to all of the problems in Chapter 9 of the NCERT textbook. Read the first theoretical chapter. Make sure you’ve gone through the theoretical section of chapter 9 in the NCERT textbook and that you know the formula for the chapter.

When working through the exercises in the NCERT textbook, if you run into any type of difficulty or uncertainty, you may use the SWC NCERT Solutions for class 8 as a point of reference. While you are reading the theory from the textbook, it is imperative that you always have notes prepared. You should make an effort to understand things from the very beginning so that you may create a solid foundation in the topic. Use the NCERT as your parent book to ensure that you have a strong foundation. After you have finished reading the theoretical section of the textbook, you should go to additional reference books.

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